Even more computer-generated knitting!

Oh, apparently I forgot to post this one here -- following the fun with the javascript hat-matron, I decided to write up another quick javascript pattern generator, this time for a less trivial pattern.
I picked the Universal Cover Scarf, since I already have that mostly coded up, and just needed to convert it across.
You can see the result here:

Scarf-matron

A friend also pointed this website out to me, which does a similar sort of thing, only much better, and in php:

Knitting fool

I particularly recommend their sweater generator, which has a huge number of variables, a selection of different constructions and even comes up with graphical representations so you can see how it all works. It's very cool!

Hugh.

Geoemtric Knitting II ... somewhat belatedly

Hi folks, I've just realised how long it's been since I've posted anything here, and I have a whole bunch of stuff waiting!

A few weeks (well, months) ago, I gave a talk in our PG Colloquium series on the subject of geometry and knitting. The idea was to show off a few mathematical knitting projects I've been playing with, and use them to illustrate some maths.
I'll write about the projects individually later, but in the meantime you can read the slides here:
Slides (pdf)

A couple of the projects used computer programs to calculate the patterns, based on inputted parameters. These programs are written in Ruby, and if you'd like to give them a try they can be found here:
Universal cover scarf
Cellular automata shawl
Hopefully their operation should be pretty clear, and is explained in more detail in the slides. If anyone's interested in knitting from these I'd be delighted to give some tips!

Also, thanks again to my Glamorous Assistant Pamela!

Also also, the Juliana hearts project is still ongoing, and open to all, so if I can send you one let me know. (Hmm, have I really not posted about that here before? More on that to follow then.)

Happy knitting, and more posts soon,
Hugh.

Universal cover scarf

Hi folks!

Continuing the mathematical theme, my next plan is to knit the universal cover of a punctured disc, arranged to make a ruffly scarf.

So, what is a universal cover? The idea is to take a space, and form a new space which is locally the same, but in which any loop can be shrunk down to a point. This is useful because when we try to extend local properties of spaces to global ones, it's usually these kind of loops which cause problems.
As an example, consider a disc with it's centre missing, the `punctured disc'. A loop in this space can be shrunk down to nothing provided it doesn't wrap around the hole. To remove these loops, imagine we take an infinite number of these discs, and declare that a path which crosses the x-axis in a clockwise direction moves one disc up the chain, and if it crosses anti-clockwise, one to the right. Now if we take a loop in this space, if it wraps round the centre point we've moved up or down the chain, so the loop is no longer closed. Then any loop in this new space corresponds to a loop on the punctured disc which doesn't wrap around the hole, and can be shrunk to a point. This space is called the universal cover of the punctured disc.
Another way to see the same space is this -- take an infinite sequence of discs, each slit along the x-axis. Glue the top edge of each slit to the bottom edge of the slit on the preceding disc. You can then stretch this out to make a sort of spirally chain, which I think would make a neat scarf.

So, how to knit this? If you imagine following a circle around the origin in this spirally chain, it will form a helix (assuming you've `stretched' the same way I have, this isn't entirely fixed) in space. My plan is for these helices to form the rows, working from the outside in. Of course, since I don't want my rows to be infinitely long I'll only have a finite number of discs in my chain.
One of the cool properties of helices is that it's quite easy to calculate their lengths (which is really quite rare among curves). Since the space is symmetric under shifting along the axis of the helices (after a suitable rotation), it's then just a matter of working out how many stitches to decrease in each row and spacing these evenly along the length. This is the same problem as knitting surfaces of revolution (see also), and it will be easy to adapt the solutions from there.
The actual maths I'll carry out using Ruby, this seems like the kind of problem it's very good at.

I should say too that I'm fairly sure this kind of scarf already exists, though without the mathematical intent. Must make sure to look around and see if I can find some links to compare with. I'm hoping that not being flat will make it nice and warm, but will have to see how it stands up to Edinburgh's winds.

Happy knitting, and/or calculating!
Hugh.